Question

A triangle has sides of lengths 5.65 and 10.75. What is the possible range for the third side?

5.1 < x < 16.4

5.65 < x < 10.75

x < 5.1 < 16.4

None of the above

Answer 1

5.1 < x < 16.4

Explanation:

If we are given 2 sides of a triangle and need to know the third side (the range of values), we can say that the third side will fall between the DIFFERENCE and SUM of the other 2 sides.

If the third side is c, and other two sides are a and b (where a < b), then the third side would be:

b - a < c < a + b

Thus, here we have third side as "x" and other 2 sides as 5.65 and 10.75, so x would be:

10.75 - 5.65 < x < 10.75 + 5.65

5.1 < x < 16.4

That's the first answer choice: 5.1 < x < 16.4